Latent Class Analysis

1. First, make sure all variables are factors and subset the data to include only LCA classification variables and covariates:

2. Second, define the LCA formula.

  • Variables in parentheses are the latent class classification variables.

  • Variables outside of the parentheses are covariates (not included in the LCA).

  • Finally, run the LCA specifying a range of classes

  • LCA: Classification VARS: ASUS / Risk/ Trauma

  • covariates: demographics (no location)

  • chisq+post-hoc: latent class vs. Outcome: Incident Score –> binary

Visualizations

Demographics

ASUS

RISK

Trauma

Incidents

Client Class Profiles

Client Class 1

## # A tibble: 3 × 2
##   class     n
##   <fct> <int>
## 1 1       905
## 2 2       467
## 3 3       442
## # A tibble: 3 × 5
##   class   min median  mean   max
##   <fct> <int>  <dbl> <dbl> <int>
## 1 1        21   41    42.6    79
## 2 2        22   40    41.9    82
## 3 3        23   44.5  44.9    68
## # A tibble: 5 × 3
##   Race                              counts percent
##   <chr>                              <int>   <dbl>
## 1 African American or Black            400    0.44
## 2 Caucasian or White                   234    0.26
## 3 Some other race                      212    0.23
## 4 Multi-Racial                          47    0.05
## 5 American Indian or Alaskan Native     12    0.01
## # A tibble: 12 × 3
##    Religion    counts percent
##    <chr>        <int>   <dbl>
##  1 None           261   0.288
##  2 Christian      216   0.239
##  3 Catholic       176   0.194
##  4 Protestant      74   0.082
##  5 Baptist         63   0.07 
##  6 Islamic         45   0.05 
##  7 Other           44   0.049
##  8 Pentecostal     10   0.011
##  9 Agnostic         6   0.007
## 10 Buddhist         5   0.006
## 11 Jewish           4   0.004
## 12 Mormon           1   0.001

Chi-square Test

## 
##  Pearson's Chi-squared test
## 
## data:  data$Incident_class and data$Client_class
## X-squared = 4.7466, df = 2, p-value = 0.09317
##                    data$Client_class
## data$Incident_class   1   2   3
##                 No  879 444 430
##                 Yes  26  23  12
##                    data$Client_class
## data$Incident_class          1          2          3
##                 No  0.97127072 0.95074946 0.97285068
##                 Yes 0.02872928 0.04925054 0.02714932
##                    data$Client_class
## data$Incident_class         1         2         3
##                 No  0.5014261 0.2532801 0.2452938
##                 Yes 0.4262295 0.3770492 0.1967213
## Adjusted p-values used the bonferroni method.
##   comparison  raw.p  adj.p
## 1    1 vs. 2 0.0646 0.1938
## 2    1 vs. 3 1.0000 1.0000
## 3    2 vs. 3 0.0876 0.2628

Client class profiles

Cluster 1 Cluster 2 Cluster 3
Number of Clients 905 467 442
Current Age 42.58 41.93 44.89
Suicide Risk Level 0.25 0.18 0.65
Homicide Risk Level 0.09 0.07 0.16
Criminal History 3.41 3.1 3
Aod Involvement 7.75 2.23 17.55
Disruption 8.5 1.35 38.52
Life Functioning Problems 33.35 10.9 81.84
Aod Last Six Months 2.47 0.33 12.52
Legal Non-Conforming Problems 2.84 1.57 4.72
Proportion with Trauma History 33% 28% 44%
## [[1]]
##  Gender                                      Race    
##  F: 24   African American or Black             :400  
##  M:881   American Indian or Alaskan Native     : 12  
##          Asian                                 :  0  
##          Caucasian or White                    :234  
##          Multi-Racial                          : 47  
##          Native Hawaiian/Other Pacific Islander:  0  
##          Some other race                       :212  
##               MaritalStatus       Religion     Discharged City
##  Civil Union         :  5   None      :261   New Haven :370   
##  Divorced/Annulled   : 78   Christian :216   Middletown: 84   
##  Legally separated   : 20   Catholic  :176   Hartford  : 61   
##  Married             : 79   Protestant: 74   Bridgeport: 46   
##  Other               :  1   Baptist   : 63   Waterbury : 28   
##  Single/Never Married:722   Islamic   : 45   (Other)   :260   
##  Widow/widower       :  0   (Other)   : 70   NA's      : 56
## [[1]]
##  Gender                                      Race    
##  F:  2   African American or Black             :225  
##  M:465   American Indian or Alaskan Native     :  0  
##          Asian                                 :  4  
##          Caucasian or White                    : 94  
##          Multi-Racial                          : 23  
##          Native Hawaiian/Other Pacific Islander:  1  
##          Some other race                       :120  
##               MaritalStatus       Religion     Discharged City
##  Civil Union         :  2   None      :139   New Haven :207   
##  Divorced/Annulled   : 52   Christian :114   Middletown: 59   
##  Legally separated   :  4   Catholic  : 70   Hartford  : 25   
##  Married             : 40   Protestant: 42   Bridgeport: 20   
##  Other               :  0   Baptist   : 32   Waterbury : 12   
##  Single/Never Married:366   Islamic   : 28   (Other)   :106   
##  Widow/widower       :  3   (Other)   : 42   NA's      : 38
## [[1]]
##  Gender                                      Race    
##  F: 29   African American or Black             : 90  
##  M:413   American Indian or Alaskan Native     :  0  
##          Asian                                 :  2  
##          Caucasian or White                    :254  
##          Multi-Racial                          : 22  
##          Native Hawaiian/Other Pacific Islander:  0  
##          Some other race                       : 74  
##               MaritalStatus       Religion     Discharged City
##  Civil Union         :  2   None      :134   New Haven :176   
##  Divorced/Annulled   : 53   Catholic  :120   Middletown: 55   
##  Legally separated   : 11   Christian : 90   Hartford  : 18   
##  Married             : 24   Protestant: 36   Waterbury : 18   
##  Other               :  1   Baptist   : 18   Bridgeport: 17   
##  Single/Never Married:343   Other     : 18   (Other)   :126   
##  Widow/widower       :  8   (Other)   : 26   NA's      : 32